Mortality-based longevity risk affects many types of financial instruments, such as life settlements. Life settlements pertain to life insurance policies that are sold by insured individuals to an investor—usually for more than the surrender value offered by the insurance company. The investor takes over responsibility for paying the premiums and becomes the beneficiary of the policy, receiving the face-value (i.e., death benefit) of the policy when the insured individual dies.
Pools of life settlements can be significantly affected by face-value variance risk and longevity risk or, put simply: who dies when. Face-value risk arises when the insured individuals underlying a pool of life settlements have policies with differing face values. Face value variance risk is sometimes called severity risk or event risk.
To illustrate each risk, one can first look at what happens if there is neither face-value risk nor longevity risk. FIG. 1 shows the most probable cash flows generated by a typical pool of $1 billion worth of life insurance written on 300 or so health-impaired individuals.
Typical pools of life settlements, including this example, start as negative yield assets. For the first year or two, nearly all the individuals are expected to remain alive and therefore the premiums must be paid to keep the policies in force. If one paid $200 million (⅕th of face value) for a pool, and yearly premiums average 5% of face value, then one will pay close to $50 million a year just to maintain the investment—at least for a few years.
Longevity risk leads to excess return or loss when the actual mortality experience of a pool differs from projected. Usually lumped together, there are actually two types of longevity risk: alpha-longevity risk and beta-longevity risk, with one compounding the other. Alpha-longevity risk arises from information asymmetries between market participants, and is akin to the alpha technical risk ratio used in the stock markets. Beta-longevity risk is the sensitivity of pool returns to changes affecting general population longevity, and parallels the beta technical risk ratio used in the stock markets.
To contrast one type of longevity risk with the other, consider a pool of life settlements linked to 300 insured individuals, each of whom is health-impaired. One might expect the pool's 300 health-impaired individuals to live, on average, 8 years, while 300 people drawn at random from the general population might live 11 years.
An example of alpha-longevity risk is the risk that one has miscalculated the degree of health impairment, or maybe a drug is invented that helps manage or cure the specific impairments of the insured individuals linked to the pool, with the result that the insured linked to the pool live 10, and not 8, years. An example of beta-longevity risk is the risk of an unexpected increase in longevity of the general population so that the individuals linked to the pool live perhaps 8.1, not 8, years.
Not only is alpha-longevity risk greater than beta-longevity risk, but also the two risks aren't necessarily correlated, and there is basis risk between them.
Medical underwriters have the job of predicting life expectancies. If a medical underwriter states that the pool has a life expectancy of 11 years, then approximately half the insured individuals will be living at the start of the 12th year. Relying on these predictions introduces both types of longevity risk.
If the pool's cash flows depended on the lives of 10,000 individuals, one might reasonably expect the smooth and predictable cash flows illustrated above in FIG. 1. Yet the pool's cash flows depend on the lives of 300 or so individuals. FIG. 2 illustrates what happens when one adds a dose of realism into the modeling.
The degree of randomness of the path is the thing to note here, not the path itself, which is just one of a near infinite number of possibilities modeled, using a combination of actual results from similar pools and stochastic techniques.
The only source of variance introduced so far comes from a lack of diversity, and the chaotic cash flow projections in FIG. 2 arise even if the medical underwriter does a perfect job and one knows for certain the average life expectancy of the pool.
Medical underwriters do not generally have enough data to do a perfect job. Systematic under- or overestimation of life expectancies is called table bias. For clarity, the next few figures show the effect of table bias on cash flow, and ignore the ever-present and compounding effect of random variance.
FIG. 3 illustrates mean-extension, which is to say that the insured linked to the pool generally live longer than the medical underwriter expects.
Mean-extension nearly halves the net present value (NPV) because the pool owner will receive cash later—and pay premiums longer—than thought.
Even if the medical underwriter correctly predicts the average life estimate, other less-obvious forms of table bias will, if overlooked, lead one to over- or underestimate the pool's NPV.
FIG. 4 shows how NPV is affected when there are fewer early mortalities than expected, an acceleration of mortalities in the middle of the pool's life, and fewer mortalities toward the end of the pool's life. The average life expectancy alone fails to warn that the NPV of the pool is nearer to $150 million than $200 million.
To help an investor better value the pool, the medical underwriter might draw the distribution for the investor, or include three other statistical measures: standard deviation, kurtosis, and skewness. Whereas standard deviation measures how tightly a distribution is clustered, kurtosis describes the degree of “pointiness” or “flatness” of a distribution, and skewness measures its lopsidedness. Statisticians refer to the shape of the distribution in FIG. 4 as leptokurtic, which roughly translates to “thinly bulging.”
FIG. 5 illustrates the inverse form of table bias to that of FIG. 4. Without knowing the standard deviation and kurtosis, one doesn't realize that the NPV of the pool is higher than one thinks it is. Statisticians refer to the squished-looking distribution in FIG. 5 as platykurtic, which means “broadly bulging”.
The variance in NPV illustrated by FIGS. 3 through 5 highlights the potential dangers in the standard industry practice of simplifying mortality distributions to a single number: the average. A mortality distribution, like any probability distribution, is a range concept, and all but the most basic require more than one statistic for proper description.
As mentioned above, alpha longevity risk arises from information asymmetries among market participants. Life settlement investors think they'll make money from insurance companies through the investors' special skills in actuarial science. However, insurance companies are also knowledgeable about actuarial science.
1. Insurance companies, intermediaries, and investors are concerned about life settlement buyers arbitraging the insurance company's lapse-based pricing model. For certain policy types, lapse rates approach 80% so the insurance company's apparent vulnerability appears to be a compelling opportunity for investors. Less widely known is that the policies written on seniors—those most likely to wind up as life settlements—can have lapse rates as low as 9%, which is a far cry from 80%. If the arbitrage is thinner than thought, the insurance company needs only to raise premiums a little to level the playing field, or even gain the upper hand.
2. Some investors assume that if the individual is health-impaired, the policy must have value. Only if the insured has become unexpectedly impaired after the policy was issued does this make sense, and aging is not unexpected. If the individual already was health-impaired when the policy was issued, then the investor is betting that the insurance company either didn't do its underwriting properly, or assumed a high lapse rate.
3. Some investors are looking at “carrier approved” premium-finance origination programs, where the insurance company is apparently aware of the high probability that the life insurance policies will be sold as life settlements. Shareholders of insurance companies are unlikely to let management write new business that will destroy shareholder value. Unless insurance companies have higher costs of capital than life settlement investors, an investment in policies that are supposedly part of carrier-endorsed origination programs may have high alpha longevity risk—unfavorable to the investor.
4. Some investors think that life settlements constitute such a small portion of the insurers' business, that insurers don't care to do much about the problem, and that insurance companies are generally slow to react to a changing marketplace that creates opportunities for investors. Insurance companies have demonstrated both that they can care greatly about small sections of their business, and that they are able to react swiftly. In the 1990s, the viatical market (predecessor of today's senior life settlement market) was all but wiped out, in part through medical advancements, but mainly through the introduction, by insurance companies, of the accelerated death benefit that is now included in most life policies.
5. Investors value a life settlement based, in part, on the impairment opinion prepared by one or more medical underwriters. The impairment opinion is based on available medical records, so a major risk to investors is the degree to which medical records do not accurately portray the health status of an individual. This is not the risk that medical records may be falsified, but the risk that they may have only limited value. For example, doctors may indicate a condition exists even when they are not too sure. Conservative diagnoses are in line with most doctors' motivation to care for patients (not investors), and avoid a negligence suit later for failing to alert a patient to the possibility of an illness or condition.
6. Medical underwriters can and do make unsystematic and systematic errors. The effects of unsystematic errors are minimized by increasing the number of unique insured underlying the pool. The effects of systematic error, or table bias, can dramatically impact the net present value of the pool as explained above.
Many policies do have value as life settlements. However, two other nonlongevity-related hurdles may affect the value: 1) the intermediaries who represent the insured also know that the policy has value; and 2) only three out of four dollars will get past the intermediaries as invested capital, so one's investment has to increase in value by one third just to break even.
Techniques to manage longevity risk include insurance and annuities, as well as new derivatives that may provide cheaper, more liquid alternatives to insurance.
Barring a cure for old age, a worldwide plague, or other global catastrophe, the chance of a small increase in longevity is closer to a certainty than a risk. Beta-longevity risk can, therefore, be managed simply by increasing the number of insured individuals underlying the pool of life settlements.
Alpha-longevity risk is not necessarily reduced through diversification, so one of the few options available to the investor is the purchase of longevity-extension insurance.
Issuers of longevity-extension insurance—otherwise known as a mortality wrap—charge the pool owner an up-front fee as high as 30% of the pool's market value. The wrap issuer agrees to purchase any outstanding polices on a future date, for an agreed value, which is usually less than the face value.
The future date is usually the pool's average life expectancy—as determined by the issuer, not the pool owner—with a couple of years tacked on for good measure. Some issuers require the owner to prepay all premiums that would fall due before the exercise date. If the average life expectancy of the pool is 10 years, then the pool owner must wait 12 years before exercise. The credit rating of the issuers is sometimes lower than AA, or the issuer may be unrated.
One might wonder why mortality wraps are so expensive. Early pool owners had more information about the insured than the issuer of the wrap, so the owners used the additional information to select the insured with a higher likelihood of outliving their life estimates. Also, sellers of policies had more information about their own health than the pool owners. Compounding the problem further was that medical underwriters had little experience forecasting the mortality of people who choose to sell their life insurance to strangers. The result was that the insured tended to outlive their life expectancies, and the wrap issuers lost money. Some issuers refused to pay, blaming the medical underwriters, so the pool owners lost, too. Today's wrap issuers are aware they'll be the targets of adverse selection, and price accordingly.
Another technique is for a pool owner to purchase an annuity to partially offset premium payments. The expected yield on the combined asset may be close to, or below, LIBOR.
Mortality wraps and annuities have been around for several years, but newly launched longevity indices are paving the way for derivative transactions, because the indices can be used as a reference value against which to settle trades. Most indices were launched by institutions whose customers are affected by longevity risk.
Longevity indices allow derivatives and hedging strategies that settle yearly—sometimes more frequently—rather than pay out once in 10 or 12 years. Some market participants who might wish to make markets in longevity risk would prefer shorter-dated exposure. A series of short-dated derivatives based on these indices could provide an alternative to mortality wraps.
The Credit Suisse Longevity Index, released in December 2005, is designed to enable the structuring and settlement of longevity risk transfer instruments, such as longevity swaps and structured notes. Credit Suisse expects their index to spur the development of a liquid, tradable market in longevity risk, as it provides a standardized measure of the expected average lifetime for general populations, based on publicly available U.S. statistics. The index includes both historical and forward values, and is released annually.
JPMorgan launched its LifeMetrics Indexsm in March 2007. An international index designed to benchmark and trade longevity risk, the index is part of a platform aimed at measuring and managing both longevity and mortality exposure. The index will enable pension plans to calibrate and hedge the risk associated with the longevity of their beneficiaries. The index incorporates historical and current statistics on mortality rates and life expectancy, across genders, ages, and nationalities.
However, the existing techniques to manage longevity risk suffer from many disadvantages. For example, mortality guaranties or puts are expensive, require upfront cash, make the credit rating of the guarantor critically important, do not solve intermediate cash short-fall problems, and generate a solution that pays out years from now, with no mark-to-market. SPIA (Single Payment Immediate Annuity) or other forms of annuity to partially or fully offset liability to pay premiums are expensive, may hinder individual policy sales as usually annuities are sold as a package, and cannot be sold per policy. With fixed-for-floating yield swaps, pools consume cash for early years, then eventually generate net cash. As a result, the fixed payer is disadvantaged in the early years. They are prone to credit rating problems and are not fungible, as the deal is asymmetric for years. Securitization and tranching are expensive and lock up policies for the entire term. With some techniques, investors learn of personally identifiable information when they don't need that information. And, as explained above, using life expectancies to price life settlements are insufficient to describe mortality distributions, because they are more or less the mean of a mortality distribution. Two different mortality distributions can have identical means, yet different timing of cash flows, leptokurtic, skew and polymodal considerations, standard deviation and other moments about the mean are not taken into account well.